Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Rowan Killip*, Tadahiro Oh, Oana Pocovnicu, Monica Visan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Gross-Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

Original languageEnglish
Pages (from-to)969-986
Number of pages18
JournalMathematical research letters
Volume19
Issue number5
DOIs
Publication statusPublished - 2012

Keywords

  • NLS
  • Gross–Pitaevskii equation
  • non-vanishing boundary condition

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